Question

he safety director of a large steel mill took samples at random from company records of minor work-related accidents and classified them according to the time the accident took place.

	Number of					Number of
Time	Accidents				Time	Accidents
8 up to 9 a.m.		10			1 up to 2 p.m.		6
9 up to 10 a.m.		6			2 up to 3 p.m.		8
10 up to 11 a.m.		6			3 up to 4 p.m.		7
11 up to 12 p.m.		16			4 up to 5 p.m.		20

Using the goodness-of-fit test and the 0.01 level of significance, determine whether the accidents are evenly distributed throughout the day.

H₀: The accidents are evenly distributed throughout the day.   
H₁: The accidents are not evenly distributed throughout the day.

a) State the decision rule, using the 0.01 significance level.

b) Compute the value of chi-square.

c)What is your decision regarding H₀?

Answer 1

A)The significance level for a given hypothesis test is a value for which a P-value less than or equal to is considered statistically significant. If the p value is 0.01 is considered significant or insignificant for confidence interval of 0.99.

B)
observed frequencies of accidents (fo)=10,6,6,16,6,8,7,20

Total of accidents are: 10+6+6+19+6+8+7+20=79

Average = 79/8

expected frequencies (fe)= 79/8,79/8,79/8,/79/8,79/8,79/8,79/8,79/8

H0: Accidents are evenly distributed throughout the day
H1: Accidents are not evenly distributed throughout the day

chi-square test -statistic =sum(fo-fe)^2/fe = 20.09

Critical value = chi-inv(0.01,7)= 18.475

C)
Since the test statistic does fall inside the rejection region, we do reject H0.
Using a 0.01 level of significance there is sufficient evidence to conclude that
the accidents are not evenly distributed throughout the day.